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Interesting thing I've noted

  1. Nov 17, 2012 #1
    2^2-1 = 2^2-1 = 1^2+2
    2^3-1 = 3^2-2 = 2^2+3
    2^5-1 = 6^2-5 = 5^2+6
    2^13-1 = 91^2-90 = 90^2+91

    I realise that x^2-(x-1)==(x-1)^2+(x)

    2,3,5 and 13 are all the powers of mersenne primes, and are Fibonacci numbers as well.
    It'd be interesting to see what's the next power of 2 that satisfies this equation.
  2. jcsd
  3. Nov 18, 2012 #2
    Hi there, you have observed some cases of powers of 2 being almost in the middle of consecutive squares, and you ask about the next occurence. A quick computer search reveals no such cases with exponent less than 1000. So unless either I or my computer made a mistake, which may very well happen, you may want to look for other patterns instead.

    What happened to your post about sums and differences of two powers? I had written a reply, including this link, and the relation 30=832-193, and some more, and then I couldnt post it.
  4. Nov 18, 2012 #3
    Sorry, I posted this to another maths forum as well, and it turns out there are no other numbers. Here's the link I was sent:
  5. Nov 18, 2012 #4
    My last post violated forum rules, I am going to repost a revised version of it. Didn't see your reply before they deleted it, unfortunately.
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